Question

factorize x⁴-(y-2z)⁴​

Answer 1

Answer:

Q1. (A) Fill in blanks with the correct tense of the verb (Past

Tense) in the brackets.

1. The door was open and a snake (enter)

the room.

2. When I was young, I (want) to be a teacher,

3. Everyone was waiting for Sanjay but he (come)

4. It (rain). So we (take) shelter under the bridge.

5. He (write) nothing when (meet ) him last week.

6. We (prepare ) for examination for four months when we

heard of their cancellation.

Q1. (A) Fill in blanks with the correct tense of the verb (Past

Tense) in the brackets.

1. The door was open and a snake (enter)

the room.

2. When I was young, I (want) to be a teacher,

3. Everyone was waiting for Sanjay but he (come)

4. It (rain). So we (take) shelter under the bridge.

5. He (write) nothing when (meet ) him last week.

6. We (prepare ) for examination for four months when we

heard of their cancellation.

Q1. (A) Fill in blanks with the correct tense of the verb (Past

Tense) in the brackets.

1. The door was open and a snake (enter)

the room.

2. When I was young, I (want) to be a teacher,

3. Everyone was waiting for Sanjay but he (come)

4. It (rain). So we (take) shelter under the bridge.

5. He (write) nothing when (meet ) him last week.

6. We (prepare ) for examination for four months when we

heard of their cancellation.

Q1. (A) Fill in blanks with the correct tense of the verb (Past

Tense) in the brackets.

1. The door was open and a snake (enter)

the room.

2. When I was young, I (want) to be a teacher,

3. Everyone was waiting for Sanjay but he (come)

4. It (rain). So we (take) shelter under the bridge.

5. He (write) nothing when (meet ) him last week.

6. We (prepare ) for examination for four months when we

heard of their cancellation.

Answer 2

Given expression:

x⁴ - (y-2z)⁴

___________________

What to do?:

Factorise the given expression

___________________

Let's do it!

Solution:

We are given that,

x⁴ - (y-2z)⁴

$\bigstar {\sf {Using\ the\ identity\ a^{2}-b^{2} = (a+b)(a-b)}}$

(x²)² - [(y-2z)²]²

Here,

a = x²

b = (y-2z)²

[x²+ (y-2z)²][x²- (y-2z)²]

☆_______________☆

Now, as we can see, we can further factorise the expression [x²- (y-2z)²] using the same identity.

$\bigstar {\sf {Using\ the\ identity\ a^{2}-b^{2} = (a+b)(a-b)}}$

Here,

a = x

a = xb = (y-2z)

[x+(y-2z)][x-(y-2z)]

(x+y-2z)(x-y+2z)

☆_______________☆

So, finally we got,

[x²+ (y-2z)²](x+y-2z)(x-y+2z)

___________________

Final answer:

Factorised form of x⁴ - (y-2z)⁴ is [x²+ (y-2z)²](x+y-2z)(x-y+2z)

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Know more!!:

How do we obtain a² - b² from (a+b)(a-b)?

Answer:

(a+b)(a-b)

☆Using distributive property:

a (a-b) + b (a-b)

a² - ab + ab - b²

(-ab) and (+ab) will be canceled out.

= a² - b²

Henceforth, we obtain, a² - b² = (a+b) (a-b) or vice-versa.